Probabilistic representation of a class of non conservative nonlinear Partial Differential Equations.

Anthony Le Cavil, Nadia Oudjane and Francesco Russo
april, 2014
Publication type:
Lecture note
Journal:
Arxiv, HAL-ENSTA
arXiv:
images/icons/icon_arxiv.png 1504.03882
Keywords :
Chaos propagation; Nonlinear Partial Differential Equations; Nonlinear Stochastic Differential Equations; Particle systems; Probabilistic representation of PDEs; McKean-Vlasov
Abstract:
We introduce a new class of nonlinear Stochastic Differential Equations in the sense of McKean, related to non conservative nonlinear Partial Differential equations (PDE). We discuss existence and uniqueness pathwise and in law under various assumptions. We propose an original interacting particle system for which we discuss the propagation of chaos. To this system, we associate a random function which is proved to converge to a solution of a regularized version of PDE.
BibTeX:
@misc{LeC-Oud-Rus-2014,
    title={Probabilistic representation of a class of non conservative 
           nonlinear Partial Differential Equations. },
    journal={Arxiv, HAL-ENSTA },
    year={2014 },
    month={4},
    comment={{umatype:'cours'}},
}